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Lecture 26

1) Phase transitions occur without chemical changes and involve changes in physical state like melting or evaporation driven by Gibbs free energy. 2) The Gibbs energy of a substance increases with increasing pressure due to increasing molar volume, but decreases with increasing temperature due to increasing molar entropy. 3) Phase diagrams map the pressure and temperature conditions where different phases of a substance are stable and show phase boundaries where two phases coexist in equilibrium.

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74 views6 pages

Lecture 26

1) Phase transitions occur without chemical changes and involve changes in physical state like melting or evaporation driven by Gibbs free energy. 2) The Gibbs energy of a substance increases with increasing pressure due to increasing molar volume, but decreases with increasing temperature due to increasing molar entropy. 3) Phase diagrams map the pressure and temperature conditions where different phases of a substance are stable and show phase boundaries where two phases coexist in equilibrium.

Uploaded by

seanivens
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as PDF, TXT or read online on Scribd
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Phase equilibria of pure substances

Atkins, Chapter 5

Phase transition: phase change without change


in chemical composition
(e.g., ice melting, evaporation + fog formation)
G
Molar Gibbs energy: Gm = extensive
intensive n
A substance has a
spontaneous tendency to
Phase 1: Phase 2: change into the phase of
water vapor water liquid lowest Gibbs energy
To occur spontaneously:
Nils Walter: Chem 260
∆G = nGm(2) - nGm(1)= n{Gm(2) - Gm(1)} < 0
The Gibbs energy “under pressure”
From G = H -TS ⇒ dG = dH - TdS - SdT
dG = Vdp - SdT and dH = dU + pdV + Vdp and dU = dw + dq
and reversible change: dq = TdS and dw = -pdV

⇒ dGm = Vmdp - SmdT = Vmdp With increasing pressure


(dp > 0) the molar Gibbs
at constant T energy increases (dG > 0)

pf pf

∆Gm = ∫ Vm dp = Vm ∫ dp = Vm ∆p
pi pi
For liquid, solid:
Vm independent of p
⇒ linear p dependence
Nils Walter: Chem 260
The Gibbs energy of gases under pressure
pf

∆Gm = Gm ( p f ) − Gm ( pi ) = ∫ Vm dp
pi
pf pf
RT dp pf
perfect gas equation = ∫ dp = RT ∫ = RT ln
pi
p pi
p pi
@ constant T

pf
Gm ( p f ) = Gm ( pi ) + RT ln
pi
As Vm gets smaller (@ higher p), Gm
becomes less responsive to pressure

Nils Walter: Chem 260


The Gibbs energy “under fire”
dGm = Vmdp - SmdT Since the molar entropy is always
= -SmdT positive, an increase in
temperature (dT > 0) always leads
@ constant p to a decrease in Gm (dGm < 0)

Sm(gas) > Sm(liquid) > Sm(solid)

CO2 sublimes
slopes

Transition
Nils Walter: Chem 260
temperatures
Luckily, there is more than
thermodynamics in life
Graphite Diamond

<20,000 bar >20,000 bar Slow kinetics


@ 1 bar: 3 kJ mol-1 make
more stable engagements
more durable...
Spontaneity (determined by ∆G) is a
tendency, not necessarily an actuality
Nils Walter: Chem 260
Phase diagrams
= maps showing p, T conditions at which the
various phases of a substance are stable
phase boundaries Cooling curve
(2 neighboring phases
coexist in equilibrium)

⇒ determination of
a phase boundary
E DB

Nils Walter: Chem 260

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